Discontinuity, Nonlinearity, and Complexity
Evolutionary Dynamics of a SingleSpecies Population Model with Multiple Delays in a Polluted Environment
Discontinuity, Nonlinearity, and Complexity 9(3) (2020) 433459  DOI:10.5890/DNC.2020.09.007
Ashok Mondal$^{1}$, A. K. Pal$^{2}$, G. P. Samanta$^{1}$
$^{1}$ Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah  711 103, India
$^{2}$ Department of Mathematics, S. A. Jaipuria College, Kolkata700005, India
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Abstract
In this work, evolutionary dynamical behaviour of a singlespecies population model in a polluted environment has been analyzed. This model system describes the effect of toxicant on a singlespecies population. Two discrete time delays have been incorporated for proper description. Important mathematical characteristics of the proposed model such as positivity, boundedness, stability and Hopfbifurcation for all possible combinations of both the delays at the interior equilibriumpoint of the model system have been discussed. It is observed that increase amount of delay may lead to the change of stable behaviour of stationary points through the creation of limit cycles and higher periodic oscillations. Furthermore, it is reported that Hopfbifurcations may also occur around stationary points for corresponding nondelayed system. Various numerical simulations are performed to validate analytical findings.
Acknowledgments
The authors are grateful to the anonymous referees and the Editor Dr. Dimitri Volchenkov, DSc, for their careful reading, valuable comments and helpful suggestions, which have helped them to improve the presentation of this work significantly. The first author (Ashok Mondal) is thankful to the University Grants Commission, India for providing SRF (RGNF).
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